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Symmetries in semidefinite programming, and how to exploit them


P.A. Parrilo

USA, Univ. of California at Berkeley, EECS Department.

Semidefinite programming (SDP) techniques have been extremely successful in many practical engineering design questions. In several of these applications, the problem structure is invariant under the action of some symmetry group, and this property is naturally inherited by the underlying optimization. A natural question, therefore, is how to exploit this information for faster, better conditioned, and more reliable algorithms. To this effect, we study the associative algebra associated with a given SDP, and show the striking advantages of a careful use of symmetries. The results are motivated and illustrated through applications of SDP and sum of squares techniques from networked control theory, analysis and design of Markov chains, and quantum information theory.


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